Deformed Weitzenb\"ock Connections and Teleparallel Gravity

TL;DR

This paper investigates conditions on a generic connection derived from the vielbein to produce theories equivalent to Einstein Gravity, including Teleparallel Gravity, with potential applications to Double Field Theory.

Contribution

It introduces a framework for analyzing connections in gravity theories, extending Teleparallel Gravity, and explores their relevance to Double Field Theory.

Findings

Derived equations of motion for new connections

Recovered Teleparallel Gravity equations as a special case

Potential applications to Double Field Theory

Abstract

We study conditions on a generic connection written in terms of first-order derivatives of the vielbein in order to obtain (possible) equivalent theories to Einstein Gravity. We derive the equations of motion for these theories which are based on the new connections. We recover the Teleparallel Gravity equations of motion as a particular case. The analysis of this work might be useful to Double Field Theory to find other connections determined in terms of the physical fields.